Stress-energy tensor of adiabatic vacuum in Friedmann-Robertson-Walker spacetimes

Journal Article · Fri Apr 01 04:00:00 EDT 2011 · Journal of Cosmology and Astroparticle Physics

DOI:https://doi.org/10.1088/1475-7516/2011/04/040· OSTI ID:22277861

Kaya, Ali; Tarman, Merve ^[1]

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1. Department of Physics, Bo g-tilde aziçi University, 34342, Bebek, İstanbul (Turkey)

We compute the leading order contribution to the stress-energy tensor corresponding to the modes of a quantum scalar field propagating in a Friedmann-Robertson-Walker universe with arbitrary coupling to the scalar curvature, whose exact mode functions can be expanded as an infinite adiabatic series. While for a massive field this is a good approximation for all modes when the mass of the field m is larger than the Hubble parameter H, for a massless field only the subhorizon modes with comoving wave-numbers larger than some fixed k{sub *} obeying k{sub *}/a > H can be analyzed in this way. As infinities coming from adiabatic zero, second and fourth order expressions are removed by adiabatic regularization, the leading order finite contribution to the stress-energy tensor is given by the adiabatic order six terms, which we determine explicitly. For massive and massless modes these have the magnitudes H{sup 6}/m{sup 2} and H{sup 6}a{sup 2}/k{sub *}{sup 2}, respectively, and higher order corrections are suppressed by additional powers of (H/m){sup 2} and (Ha/k{sub *}){sup 2}. When the scale factor in the conformal time η is a simple power a(η) = (1/η){sup n}, the stress-energy tensor obeys P = Øρ with Ø = (n−2)/n for massive and Ø = (n−6)/(3n) for massless modes. In that case, the adiabaticity is eventually lost when 0 < n < 1 for massive and when 0 < n < 3/2 for massless fields since in time H/m and Ha/k{sub *} become order one. We discuss the implications of these results for de Sitter and other cosmologically relevant spaces.

• OSTI ID: 22277861
• Journal Information: Journal of Cosmology and Astroparticle Physics, Journal Name: Journal of Cosmology and Astroparticle Physics Journal Issue: 04 Vol. 2011; ISSN 1475-7516
• Country of Publication: United States
• Language: English

Related Subjects

79 ASTRONOMY AND ASTROPHYSICS
APPROXIMATIONS
ASTROPHYSICS
CORRECTIONS
COSMOLOGICAL MODELS
COSMOLOGY
COUPLING
DE SITTER GROUP
DE SITTER SPACE
MASS
SCALAR FIELDS
SCALARS
SPACE-TIME
STRESSES
TENSORS
UNIVERSE